Research in social sciences: Fuzzy regression and causal complexity

Abstract

Social science research is now primarily divided into two types: qualitative, or case-oriented research, focused on individual cases, which reviews all aspects of a few case studies and quantitative, or variable-oriented research, which considers only some quantitative aspects (variables) of a large number of cases and is looking for correlations between these variables. The first type of research is based primarily on evidence, the second on theoretical models. The fundamental criticism to case-oriented research is that it does not lead to general theoretical models, while the most important criticisms to the variable-oriented research are the assumption of a population a priori and the hypothesis that the elements of the population are homogeneous. A compromise between the two points of view is the diversity-oriented research, which takes into account the variables and the diversity of individual cases. The fundamental purpose of our paper is to study the possibilities provided by fuzzy sets and algebra of fuzzy numbers for the study of social phenomena. We deepen some aspects of the fuzzy regression, and we present some operations between fuzzy numbers that are efficient alternatives to those based on Zadeh extension principle. Finally, we present some critical remarks about the causal complexity and logical limits of the assumption of linear relationship between variables. A solution of these problems can be obtained by the fuzzy sets that play a key role in diversity-oriented research. © Springer-Verlag Berlin Heidelberg 2013.